24 Numerics library [numerics]

24.9 Mathematical functions for floating-point types [c.math]

24.9.5 Mathematical special functions [sf.cmath]

24.9.5.12 Incomplete elliptic integral of the second kind [sf.cmath.ellint_2]

double       ellint_2(double k, double phi);
float        ellint_2f(float k, float phi);
long double  ellint_2l(long double k, long double phi);

Effects: These functions compute the incomplete elliptic integral of the second kind of their respective arguments k and phi (phi measured in radians).

Returns:

$E (k, ϕ) = \int_{0}^{ϕ} \sqrt{1 - k^{2} sin^{2} θ} d θ, for | k | \leq 1,$

where k is k and φ is phi.